WKB approximation for analyzing quantum tunneling effect through negative Kratzer potential

Abstract

Abstract Kratzer potential is a potential for bound states in molecular bonds, while negative Kratzer potential is a potential for scattering states which has a barrier form, and which clearly has properties opposite to the bound state potential. This type of potential is the main subject of this paper. When a non-relativistic particle which has lower energy moving towards the potential, then there is a probability for the particle to break through the potential. In this paper, we use the WKB (Wenztel-Kramers-Brillouin) method to analyze the physical conditions that must be met by the system in order for the tunneling processes to occur. We present these conditions in the form of the relationship among several quantum variables such as the mass of the particle, the energy of the particle, the maximum height of the barrier potential, equilibrium internuclear separation, and the enactment domain of the potential field effect on the particle when the particle breaks through that potential.